2018/05/23 by Maria Vasilyeva, Vasilyeva, Maria, Eric T. Chung +5
Computer Science · Engineering · #Advanced Mathematical Modeling in Engineering #Composite Material Mechanics #FOS: Mathematics #Hydraulic Fracturing and Reservoir Analysis #Numerical Analysis (math.NA)
paper · pdf · doi:10.48550/arxiv.1805.09407
openalex publication_date 2018/05/23 · openalex created_date 2022/10/01 · openalex updated_date 2026/07/28
In this work, we present an upscaled model for mixed dimensional coupled flow\nproblem in fractured porous media. We consider both embedded and discrete\nfracture models (EFM and DFM) as fine scale models which contain coupled system\nof equations. For fine grid discretization, we use a conservative finite-volume\napproximation. We construct an upscaled model using the non-local\nmulticontinuum (NLMC) method for the coupled system. The proposed upscaled\nmodel is based on a set of simplified multiscale basis functions for the\nauxiliary space and a constraint energy minimization principle for the\nconstruction of multiscale basis functions. Using the constructed\nNLMC-multiscale basis functions, we obtain an accurate coarse grid upscaled\nmodel. We present numerical results for both fine-grid models and upscaled\ncoarse-grid models using our NLMC method. We consider model problems with (1)\ndiscrete fracture fine grid model with low and high permeable fractures; (2)\nembedded fine grid model for two types of geometries with differnet fracture\nnetworks and (3) embedded fracture fine grid model with heterogeneous\npermeability. The simulations using the upscaled model provide very accurate\nsolutions with significant reduction in the dimension of the problem.\n